Unless the McDonald's restaurant was badly sited originally or
the town has grown in a particular direction (in which case c
would be best), probably the most strategic choice Burger King
can make is to build its restaurant next door to the McDonald's
(b). That way, Burger King provides people a choice, and
the two restaurants will come close to splitting the customer
base. (Of course, if the current position of the McDonald's
leaves a large area of town for Burger King to capture, then the
Home of the Whopper may best be placed in that unserved area.)

The origin of the insight of co-location is work done by the
economist Harold Hotelling in 1929. Hotelling drew an analogy
with an ice cream vendor who sets up a stand in the middle of a
long strand of beach, along which customers (bathers) are
uniformly distributed. A competitor arrives, hoping to capture
some of the ice cream trade from the original server. The best
position for the new vendor, Hotelling noted, is back-to-back
with the well-positioned first vendor, allowing an even split of
the market. Any other position of the new vendor would have given
that new entrant a smaller market share.

You can observe Hotelling's observation in action any time you
drive by a cluster of fast food outlets.

The problem becomes more complex when multiple servers, or
restaurants, want to enter a market of population areas (nodes)
in which a number of original servers are already operating. Say,
for instance, that Burger King wants to open four new restaurants
in a county in which four McDonald's restaurants are already
doing well. About 10 years ago, I developed a general method to
site new servers no matter what the network looks like or where
the initial servers were positioned.

According to my method, new servers (circles 27 and 8) end up
with healthy market shares (the nodes within the dotted lines),
while original server (triangle 29) is left with almost
nothing.

Sometimes a firm can even compete with itself, and it comes about
this way. When a firm like Pizza Hut allows a franchise to open
in a particular area, the expectation is that there is an
adequate customer base. As more business people apply for
franchises in the area and open their Pizza Huts, patrons tend to
go to their closest restaurant when the pizza craving hits them.
This causes the customer base to be divided amongst all the
franchises, and profits and return on investment decline. The
problem to be solved is how to allocate franchises so that the
customer base never gets diluted too much between the various
restaurants. That's a problem we're working on now.